{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PFNO3VSKLHUWAELRTMU4A2UAIQ","short_pith_number":"pith:PFNO3VSK","schema_version":"1.0","canonical_sha256":"795aedd64a59e96011719b29c06a80443cab7bc36988e2b9ad058d09477bcabd","source":{"kind":"arxiv","id":"1307.5876","version":1},"attestation_state":"computed","paper":{"title":"Selfdecomposability, perpetuity and stopping times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Zbigniew J. Jurek","submitted_at":"2013-07-22T20:34:24Z","abstract_excerpt":"In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually the later follows the first one. Equations, in question, involve the multiplication by the positive scalars $c$ or an action of the corresponding dilation $T_{c}$ on measures. In such a setting, it seems that there is no way for stopping times (or in general, for the stochastic analysis) to come into the \"picture\". However, if one accepts the view that the pri"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.5876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-22T20:34:24Z","cross_cats_sorted":[],"title_canon_sha256":"e736d8509f2076113d9922cdc0399f9ec1dab6f7e2aa8b9490408474c49add04","abstract_canon_sha256":"1127555460b0052a3afe027d8e3d336d151284b3c85507bc3903825e73f67260"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:45.912896Z","signature_b64":"LAg/EDg6dD334JS977xB6RFBfvwiyqdGkDfpNFpz+q4/DwfVVYPZJl0AxeMDb0sDVN/ZAkHGbzoZ+pdD0lOwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"795aedd64a59e96011719b29c06a80443cab7bc36988e2b9ad058d09477bcabd","last_reissued_at":"2026-05-18T03:17:45.912207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:45.912207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Selfdecomposability, perpetuity and stopping times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Zbigniew J. Jurek","submitted_at":"2013-07-22T20:34:24Z","abstract_excerpt":"In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually the later follows the first one. Equations, in question, involve the multiplication by the positive scalars $c$ or an action of the corresponding dilation $T_{c}$ on measures. In such a setting, it seems that there is no way for stopping times (or in general, for the stochastic analysis) to come into the \"picture\". However, if one accepts the view that the pri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5876","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.5876","created_at":"2026-05-18T03:17:45.912295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.5876v1","created_at":"2026-05-18T03:17:45.912295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5876","created_at":"2026-05-18T03:17:45.912295+00:00"},{"alias_kind":"pith_short_12","alias_value":"PFNO3VSKLHUW","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PFNO3VSKLHUWAELR","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PFNO3VSK","created_at":"2026-05-18T12:27:54.935989+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PFNO3VSKLHUWAELRTMU4A2UAIQ","json":"https://pith.science/pith/PFNO3VSKLHUWAELRTMU4A2UAIQ.json","graph_json":"https://pith.science/api/pith-number/PFNO3VSKLHUWAELRTMU4A2UAIQ/graph.json","events_json":"https://pith.science/api/pith-number/PFNO3VSKLHUWAELRTMU4A2UAIQ/events.json","paper":"https://pith.science/paper/PFNO3VSK"},"agent_actions":{"view_html":"https://pith.science/pith/PFNO3VSKLHUWAELRTMU4A2UAIQ","download_json":"https://pith.science/pith/PFNO3VSKLHUWAELRTMU4A2UAIQ.json","view_paper":"https://pith.science/paper/PFNO3VSK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.5876&json=true","fetch_graph":"https://pith.science/api/pith-number/PFNO3VSKLHUWAELRTMU4A2UAIQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PFNO3VSKLHUWAELRTMU4A2UAIQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PFNO3VSKLHUWAELRTMU4A2UAIQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PFNO3VSKLHUWAELRTMU4A2UAIQ/action/storage_attestation","attest_author":"https://pith.science/pith/PFNO3VSKLHUWAELRTMU4A2UAIQ/action/author_attestation","sign_citation":"https://pith.science/pith/PFNO3VSKLHUWAELRTMU4A2UAIQ/action/citation_signature","submit_replication":"https://pith.science/pith/PFNO3VSKLHUWAELRTMU4A2UAIQ/action/replication_record"}},"created_at":"2026-05-18T03:17:45.912295+00:00","updated_at":"2026-05-18T03:17:45.912295+00:00"}